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Question
If \[\tan A = \frac{5}{12}\] \[\tan A = \frac{5}{12}\] find the value of (sin A + cos A) sec A.
Solution
Given: tan` A=5/12`
`"Perpendicular"/"Base"=5/12`
`"Perpendicular"=5`
`Base=12`
`"Hypotenuse"= sqrt(("Perpendicular")^2+("Base")^2)`
We know that: ` tan A="Perpendicular"/"Base"`
`"Hypotenuse"=sqrt((5)^2+(12)^2)`
`"Hypotenuse"=sqrt169`
`"Hypotenuse"=13`
Now we find, `(sin A+cos A) SecA`
⇒ `(Sin A+Cos A)Sec A=(5/13+12/13)xx13/12`
⇒ `(sin A+cos A)sec A=17/13xx13/12`
⇒ `(sin A+cos A) sec A=17/12`
Hence the value of` (sin A+ cos A)sec A "is" 17/12`
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